9p^2+5p-3=0

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Solution for 9p^2+5p-3=0 equation: 


Simplifying
9p2 + 5p + -3 = 0

Reorder the terms:
-3 + 5p + 9p2 = 0

Solving
-3 + 5p + 9p2 = 0

Solving for variable 'p'.

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
-0.3333333333 + 0.5555555556p + p2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 0.5555555556p + 0.3333333333 + p2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 0.5555555556p + p2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 0.5555555556p + p2 = 0 + 0.3333333333
0.5555555556p + p2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
0.5555555556p + p2 = 0.3333333333

The p term is 0.5555555556p.  Take half its coefficient (0.2777777778).
Square it (0.07716049384) and add it to both sides.

Add '0.07716049384' to each side of the equation.
0.5555555556p + 0.07716049384 + p2 = 0.3333333333 + 0.07716049384

Reorder the terms:
0.07716049384 + 0.5555555556p + p2 = 0.3333333333 + 0.07716049384

Combine like terms: 0.3333333333 + 0.07716049384 = 0.41049382714
0.07716049384 + 0.5555555556p + p2 = 0.41049382714

Factor a perfect square on the left side:
(p + 0.2777777778)(p + 0.2777777778) = 0.41049382714

Calculate the square root of the right side: 0.640697922

Break this problem into two subproblems by setting 
(p + 0.2777777778) equal to 0.640697922 and -0.640697922.


Subproblem 1
p + 0.2777777778 = 0.640697922

Simplifying
p + 0.2777777778 = 0.640697922

Reorder the terms:
0.2777777778 + p = 0.640697922

Solving
0.2777777778 + p = 0.640697922

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '-0.2777777778' to each side of the equation.
0.2777777778 + -0.2777777778 + p = 0.640697922 + -0.2777777778

Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000
0.0000000000 + p = 0.640697922 + -0.2777777778
p = 0.640697922 + -0.2777777778

Combine like terms: 0.640697922 + -0.2777777778 = 0.3629201442
p = 0.3629201442

Simplifying
p = 0.3629201442


Subproblem 2
p + 0.2777777778 = -0.640697922

Simplifying
p + 0.2777777778 = -0.640697922

Reorder the terms:
0.2777777778 + p = -0.640697922

Solving
0.2777777778 + p = -0.640697922

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '-0.2777777778' to each side of the equation.
0.2777777778 + -0.2777777778 + p = -0.640697922 + -0.2777777778

Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000
0.0000000000 + p = -0.640697922 + -0.2777777778
p = -0.640697922 + -0.2777777778

Combine like terms: -0.640697922 + -0.2777777778 = -0.9184756998
p = -0.9184756998

Simplifying
p = -0.9184756998


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.3629201442, -0.9184756998}

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